cp's OEIS Frontend

A344530 For any number n with binary expansion Sum_{k = 1..m} 2^e_k (where 0 <= e_1 < ... < e_m), a(n) = Product_{k = 1..m} prime(1+e_k)^k (where prime(k) denotes the k-th prime number).

%I A344530 #11 May 24 2021 10:14:11
%S A344530 1,2,3,18,5,50,75,2250,7,98,147,6174,245,17150,25725,5402250,11,242,
%T A344530 363,23958,605,66550,99825,32942250,847,130438,195657,90393534,326095,
%U A344530 251093150,376639725,870037764750,13,338,507,39546,845,109850,164775,64262250,1183
%N A344530 For any number n with binary expansion Sum_{k = 1..m} 2^e_k (where 0 <= e_1 < ... < e_m), a(n) = Product_{k = 1..m} prime(1+e_k)^k (where prime(k) denotes the k-th prime number).
%C A344530 All terms are distinct and belong to A304678.
%H A344530 Rémy Sigrist, <a href="/A344530/b344530.txt">Table of n, a(n) for n = 0..8192</a>
%F A344530 a(0) = 1.
%F A344530 a(2*n) = A003961(a(n)).
%F A344530 a(2*n + 1) = A045967(a(n)).
%F A344530 a(2^n) = prime(n+1) for any n >= 0.
%F A344530 a(2^n - 1) = A076954(n) for any n >= 0.
%e A344530 For n = 42:
%e A344530 - 42 = 2^1 + 2^3 + 2^5,
%e A344530 - a(42) = prime(1+1) * prime(1+3)^2 * prime(1+5)^3,
%e A344530 - a(42) = 3 * 7^2 * 13^3 = 322959.
%o A344530 (PARI) a(n) = { my (v=1, e); for (k=1, oo, if (n==0, return (v), n-=2^e=valuation(n, 2); v*=prime(1+e)^k)) }
%Y A344530 Cf. A003961, A045967, A076954, A304678.
%K A344530 nonn,base
%O A344530 0,2
%A A344530 _Rémy Sigrist_, May 22 2021